Geodesic
Higher-twisted periodic smooth Deligne cohomology
Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 129-159.

Voir la notice de l'article provenant de la source International Press of Boston

Generalizing degree one twisting of Deligne cohomology, as a differential refinement of integral cohomology, from previous work, here we consider higher degree twists. The Rham complex, hence de Rham cohomology, admits twists of any odd degree. However, in order to consider twists of integral cohomology we need a periodic version. Combining the periodic versions of both ingredients leads us to introduce a periodic form of Deligne cohomology. We demonstrate that this theory indeed admits a twist by a gerbe of any odd degree. We present the main properties of the new theory and illustrate its use with examples and computations, mainly via a corresponding twisted differential Atiyah–Hirzebruch spectral sequence.
DOI : 10.4310/HHA.2019.v21.n1.a7
Classification : 14D23, 14F43, 18G40, 19L50, 53C08, 55R20
Keywords: Deligne cohomology, differential cohomology, gerbe, twisted cohomology, stack, Atiyah–Hirzebruch spectral sequence 
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     author = {Daniel Grady and Hisham Sati},
     title = {Higher-twisted periodic smooth {Deligne} cohomology},
     journal = {Homology, homotopy, and applications},
     pages = {129--159},
     publisher = {mathdoc},
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     number = {1},
     year = {2019},
     doi = {10.4310/HHA.2019.v21.n1.a7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a7/}
}
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Daniel Grady; Hisham Sati. Higher-twisted periodic smooth Deligne cohomology. Homology, homotopy, and applications, Tome 21 (2019) no. 1, pp. 129-159. doi : 10.4310/HHA.2019.v21.n1.a7. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2019.v21.n1.a7/

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